In this letter, we approach the determination of an effective interaction among phase singularities in a quantitative way.
We use a reverse-engineering approach [1]} to compute an effective pair-interaction for phase singularities in scalar random waves.
Starting with an initial guess for the pair-interaction, we use an iterative approach to amend the interaction potential until the potential generates an equilibrium configuration consistent with the input pair correlation.
We perform this procedure in the canonical ensemble, i.e., for a fixed number of singularities in a given observation area.
With this choice, we are able to converge to a stable solution for the effective interaction among pairs of singularities, also taking into account their topological charge.
Performing a final Monte Carlo simulation, using the solution for the effective interaction as an input, we are able to reproduce the theoretical pair correlation of phase singularities in random waves with excellent consistency. The method that we show here is general, and could also be applied to other systems than phase singularities in random waves.
